Bolt Preload Identification Method Based on Multi-Frequency Guided Wave Reconstruction and Spectral Centroid Fusion.

Bolted joints are critical load-transfer components in bridges, wind turbines, aerospace systems, mechanical equipment, and offshore platforms, where preload loss can degrade stiffness, accelerate fatigue, and compromise safety. For structural health monitoring, early monitoring of preload reduction before marked loosening is essential, yet existing ultrasonic guided wave indicators remain affected by frequency dependence, non-monotonic responses, amplitude drift, and environmental disturbances. This study proposes an early-warning-oriented preload identification method that combines broadband excitation, multi-frequency narrowband reconstruction, spectral centroid extraction, optimized weighted fusion, and fixed SC-domain linear calibration from one reference loading group. Using a 20-250 kHz Chirp response, 14 narrowband signals from 50 to 180 kHz were reconstructed for an M20 single-bolt specimen tested over 50-90 N·m. The fused spectral centroid index exhibited a stable, monotonic, and approximately linear relationship with preload. When fixed weights and calibration coefficients were transferred to held-out repeated-loading groups, all Pearson correlation coefficients exceeded 0.99. Feature-level robustness tests showed that the arithmetic mean of the spectral centroid reduced temperature-induced